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At least 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Analysis and Recommendation of Tritium Gas Continuous Air Monitor Alarm Setpoints for the RPL Stack Exhaust

The Radiochemical Processing Laboratory (RPL) tritium continuous air monitor (CAM) is used for near real-time detection of tritium gas (i.e., elemental tritium [HT] and tritiated water vapor [HTO]) in the stack exhaust. The CAM interfaces with software developed by the Pacific Northwest National Laboratory (PNNL)—called the “PNNL OS3700 Tritium Monitoring Software”—that provides near real-time estimates of tritium gas air concentrations and integrated daily activities that are calculated from measured CAM counts. The OS3700 software implements alarm setpoints to alert the facility of larger tritium gas releases that if allowed to persist, could begin to challenge permitted emission and established dose constraints. This report performs a detailed review of historical and current tritium alarm setpoints used at RPL, including discussion of the technical basis used in their development, analysis of alarm frequencies using measured historical data, and performs a detailed dose assessment using more realistic release scenarios and meteorology. Based on the results, the tritium air concentration and integrated daily tritium activity alarm setpoints will remain 2.0 × 10 -5 µCi/ml and 25 Ci/day, respectively. These setpoints achieve the right operational balance in identifying larger releases from planned tritium work at RPL, without being overly conservative so as to cause nuisance alarming. Furthermore, implied doses associated with these setpoints are well below defined and regulatory limits.

325RPL↗
DOE OSTI2022

Heavy Duty Natural Gas Single Cylinder Research Engine Installation, Commissioning, and Baseline Testing

Natural Gas (NG) Internal Combustion Engines (ICE) are a promising alternative to diesel engines for on-road heavy-duty applications to reduce greenhouse gas and harmful pollutant emissions. NG engines have not been widely adopted due to the lower thermal efficiency compared with diesel engine counterparts. To develop the base knowledge required to reach the desired efficiency, a Single Cylinder Engine (SCE) is the most effective platform to acquire reliable and repeatable data. A SCE test cell was developed using a Cummins 15-liter six-cylinder heavy-duty engine block modified to fire one cylinder (2.5-liter displacement). A Woodward Large Engine Control Module (LECM) is integrated to permit implementation of real-time advanced combustion control. Intake and exhaust characteristics, fuel composition, and exhaust gas recirculated substitution rate (EGR) are fully adjustable. A high-speed data acquisition system acquires in-cylinder, intake, and exhaust pressure for combustion analysis. The baseline testing shows reliable and consistent results for engine thermal efficiency, indicated mean effective pressure (IMEP), and coefficient of variance of the IMEP over a wide range of operating conditions while achieving effective control of all engine control and operation variables. This test cell will be used to conduct a research program to develop new and innovative control algorithms and CFD optimized combustion chamber designs, allowing ultra-high efficiency and low emissions for NG ICE heavy-duty on-road applications.

03 NATURAL GAS↗
DOE OSTI2022

Backpack electrofishing does not contribute to external signs of gas bubble trauma in sculpins

Abstract We exposed prickly sculpin Cottus asper and reticulate sculpin Cottus perplexus to electroshock and sham treatments in a controlled laboratory setting to determine if backpack electrofishing contributed to or exacerbated external signs of gas bubble trauma (GBT) in fish exposed to elevated total dissolved gas (TDG) levels. Fish were exposed to 115, 120 and 125% TDG (measured as percent of saturation) for various amounts of time (24–144 h) then subjected to a 5‐s electroshock or sham treatment of no electroshock. Fish were examined to determine the incidence of GBT pre‐ and post‐treatment, and all aspects (i.e., dorsal, ventral, left and right sides) of each fish were photographed. Across all TDG levels in all trials, no sculpin showed any change in GBT incidence following treatment. Analysis of GBT signs evident in photographs of 68 fish found no evidence of change in mean pre‐ and post‐treatment gas bubble sizes in fish in any TDG trial, nor were any new gas bubbles found following treatment. We are aware of no physiological mechanism by which backpack electrofishing can cause GBT in sculpin, and as such, we believe using this gear should not increase GBT incidence rates in sculpin.

Tiffan, Kenneth F.↗
DOE OSTI2023

PDMS ‐silica composite gas separation membranes by direct ink writing

Abstract Polydimethylsiloxane (PDMS)‐based membranes containing amine‐functionalized and unfunctionalized silica particles were fabricated via direct ink writing for CO 2 /N 2 gas separation. The printability of the inks was evaluated by rheological measurements, while spectroscopy, microscopy, thermal measurements, and mechanical testing were employed to characterize the printed membranes. The surface morphology of the membranes revealed the absence of voids, demonstrating their suitability for gas separation. The printed membranes also exhibited desirable thermal and mechanical properties (i.e., thermal degradation temperature of 518 °C and tensile strength as high as 1.178 MPa with 529% elongation). The PDMS‐based membranes generally displayed high permeability for CO 2 but slightly low selectivity for the CO 2 /N 2 gas pair. The best‐combined permeability‐selectivity performance of 8794 barrer and selectivity of 11.64 was demonstrated by the printed PDMS membrane containing no SiO 2 fillers. The inclusion of unfunctionalized SiO 2 particles generally increased the membrane's gas permeability but compromised the selectivity. In contrast, membranes with amine‐functionalized silica showed improved selectivity compared to membranes containing unfunctionalized silica. Overall, the performance and characteristics offered by the PDMS/silica composite membranes demonstrated the potential of 3D printing as an economical and sustainable fabrication approach to developing materials for carbon capture applications.

Gutierrez, Dianne B.↗
DOE OSTI2021

Switching CO 2 Electroreduction Selectivity Between C 1 and C 2 Hydrocarbons on Cu Gas-Diffusion Electrodes

We report that regulating the selectivity toward a target hydrocarbon product is still the focus of CO 2 electroreduction. Here, we discover that the original surface Cu species in Cu gas-diffusion electrodes plays a more important role than the surface roughness, local pH, and facet in governing the selectivity toward C 1 or C 2 hydrocarbons. The selectivity toward C 2 H 4 progressively increases, while CH 4 decreases steadily upon lowering the Cu oxidation species fraction. At a relatively low electrodeposition voltage of 1.5 V, the Cu gas-diffusion electrode with the highest Cu δ+ /Cu 0 ratio favors the pathways of hydrogenation to form CH 4 with maximum Faradaic efficiency of 65.4% and partial current density of 228 mA cm -2 at -0.83 V vs RHE. At 2.0 V, the Cu gas-diffusion electrode with the lowest Cu δ+ /Cu 0 ratio prefers C–C coupling to form C 2+ products with Faradaic efficiency topping 80.1% at -0.75 V vs RHE, where the Faradaic efficiency of C 2 H 4 accounts for 46.4% and the partial current density of C 2 H 4 achieves 279 mA cm -2 . This work demonstrates that the selectivity from CH 4 to C 2 H 4 is switchable by tuning surface Cu species composition of Cu gas-diffusion electrodes.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Surface modification of ZIF ‐90 with triptycene for enhanced interfacial interaction in mixed‐matrix membranes for gas separation

Abstract Zeolite imidazole framework (ZIF‐90) nanoparticles were chemically modified by grafting triptycene moieties. The modified nanoparticles were introduced into a triptycene‐based polyimide as fillers to generate mixed matrix membranes (MMMs) for gas separation. The incorporation of “hook‐like” triptycene moieties in both dispersed and continuous phases led to intimate contact between the two phases and thus defect‐free interfacial morphology, due to the supramolecular interlocking and π–π stacking interaction between triptycene units presented in both phases. The filler/polymer solution showed shear thickening behavior due to such strong interfacial interaction. The separation performance of the prepared composite membranes was investigated as a function of filler loading and particle surface grafting density. Pure‐gas permeation results showed that the gas permeabilities increased expectedly as the filler loading increased, with stable or improved selectivities. The reduced permeability relative to pristine polyimide film is likely due to the pore blockage of ZIF‐90 upon grafting triptycene moieties on the particle surface. Reducing the grafting density of triptycene moieties led to improved permeability and selectivity suggesting good tunability of this series of new composite membranes. Overall, modification of nanofiller with hierarchical triptycene moieties offers a fundamentally new avenue for creation of composite membranes with unique properties in gas separations.

Zhang, Qinnan↗
DOE OSTI2020

Evaluating the impact of functional groups on membrane‐mediated CO 2 / N 2 gas separations using a common polymer backbone

Abstract Polymeric membranes have shown tremendous promise for the separation of CO 2 from flue gas streams. However, few systematic studies have been conducted to better understand the impact that chemical functionalities have on membrane‐based gas separation performance. To address this gap, we herein describe the synthesis and gas separation performance of a series of vinyl‐addition polynorbornenes bearing various CO 2 ‐philic functional groups. To facilitate direct comparison between functional groups, each material was designed to maintain a common polymer backbone. Though the incorporation of CO 2 ‐philic moieties within a dense polymeric membrane is frequently hypothesized to enhance CO 2 solubility, and thereby increase CO 2 /N 2 selectivity, our results demonstrate that the incorporation of CO 2 ‐philic groups onto a common polymer backbone do not necessarily result in increased gas separation performance. Experimental and computational results demonstrate that the incorporation of amidoxime groups onto a polynorbornene backbone increase CO 2 /N 2 selectivity, whereas commonly employed ethereal side chains only increased permeability.

Higgins, Morgan A.↗
DOE OSTI2020

An experimental investigation of the effectiveness of Ar-CO 2 shielding gas mixture for the wire arc additive process

Wire arc additive manufacturing (AM) is the process by which a large, metallic structure is built layer-by-layer using a welding arc to melt a wire feedstock. A novel opportunity exists to alter the shielding gas composition to fabricate distinct geometrical features without altering the other AM parameters. In this paper, shielding gases with varied concentrations of Argon (Ar) and CO 2 was used to deposit three distinct geometric shapes (walls, infill, and overhang) using a wire-based additive manufacturing system utilizing the gas metal arc welding (GMAW) surface tension transfer (STT) process. Computer-aided design (CAD) models were sliced with a custom-built slicer, and the sliced algorithm was converted into optimal robotic toolpaths. A custom virtual instrument (VI) was built in LabVIEW to compare the temperature profiles on the surface during each deposition process. After each deposition, the geometric features were scanned, and the surface waviness value was evaluated. Tensile and Charpy impact coupons were extracted from the wall geometries in the longitudinal and transverse directions and tested. The results indicated that a higher CO 2 content produced higher melt pool temperatures to an extent, while lower contents of CO 2 resulted in a dimensionally accurate geometry. The data also indicated that the 2%/98% CO 2 /Ar blend produced scatter in tensile strength and the analysis of variance (ANOVA) shows significant difference. However, the intermediate range of CO 2 (5–10%) resulted in uniform tensile properties. Altogether, these results indicate that a 5%/95% CO 2 /Ar blend is the ideal shielding gas for lowering process temperatures and improving mechanical properties in wire arc additive manufacturing using the gas metal arc welding surface tension transfer process. Additionally, varying concentrations of Ar/CO 2 can be used within the same part in order to modify the local properties or process parameters such as strength, toughness, temperature, or dimensional features. This may improve overall manufacturing quality without sacrificing specific properties.

42 ENGINEERING↗
DOE OSTI2022

Using groundwater noble gas measurements to confirm paleorecharge hypotheses at Pahute Mesa, Nevada National Security Site, Nevada, USA

Pahute Mesa (Nevada, USA) was the site of 85 underground nuclear tests between 1965 and 1992 whose residual radio-chemical inventory poses a contaminant threat to local groundwater resources. To assess the fate and transport of these radionuclides in groundwater, several geochemical studies, including this one, have been conducted to understand long-term groundwater flow patterns at, and downgradient of, Pahute Mesa. Groundwater samples from the Pahute Mesa area at the Nevada National Security Site were analyzed for noble gases ( 3 He/ 4 He isotopic ratio and He, Ne, Kr, Ar and Xe concentrations) to infer groundwater recharge temperatures and provide additional evidence in support of groundwater flow patterns and the presence of late-pluvial Pleistocene groundwater. These data confirm recent findings (based on groundwater geochemistry and isotope compositions) that most recharge in the area occurred under temperature conditions much cooler than are found today, except near major drainages where ephemeral run of continues to recharge shallow groundwater. These noble gas data indicate that noble gas recharge temperatures and terrigenic He components have been reset where groundwater has flowed upward over barriers formed by caldera margins, or near the regional discharge area (Oasis Valley) where shallow groundwater has interacted with shallow soil gas. This evidence from groundwater noble gas measurements, in combination with other isotopic and geochemical studies, supports the current understanding of the unusual hydrogeology and recharge history of Pahute Mesa.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Modelling the complex evaporated gas flow and its impact on particle spattering during laser powder bed fusion

The additive manufacturing (AM) of metals is becoming an increasingly important production process with the potential to replace traditional techniques such as casting. Laser Powder Bed Fusion (LPBF) is used in many applications to print metal parts from powder. The metal powder is heated locally with sufficient laser radiation that the liquid melt easily reaches its boiling temperature, which leads to a metallic vapour jet that can entrain both powder bed particles and molten droplets. The small size of laser-matter interaction site makes a detailed experimental analysis of the process challenging. Synchrotron X-ray imaging experiments are one of the few methods which can capture the dynamic melting and solidification processes. Comparing such experiments with computer simulations of the process is an important approach in order to better understand the manufacturing process and to analyse the influence of process parameters on the evaporated gas jet and the subsequent impact on particle ejection, leading to potentially reduced AM component quality. The melting and solidification of the metal powder is simulated using an Eulerian multiphase approach based on a control volume discretization of powder bed and substrate and a volume of liquid separation from melt and gas phase. The gas phase modelled as an ideal gas reaches velocities up to 100 m/s. Lagrangian particle tracking in the simulation demonstrates that the velocity fields calculated by the Eulerian multi-phase approach in combination with a standard drag-force model lead to particle accelerations in good agreement with those measured experimentally. In order to avoid numerical laborious Lagrangian calculations, a direct method to compare an Eulerian multiphase simulation with synchrotron X-ray experiments was introduced and validated. This approach is used to analyse the influence of process parameters including laser power and laser speed on the maximal acceleration of particles from the melt pool area. While the particle acceleration increases linearly with line energy in the conduction mode, a linear decrease of the acceleration with increasing line energy can be found in the transition mode before the accel-eration increases again with line energy in the keyhole mode.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Printed graphene oxide-based membranes for gas separation and carbon capture

Graphene oxide (GO)-based separation membranes have demonstrated the great potential to separate molecules and ions by the interlayer spacing with tunable nano-sized channels. The scalable fabrication of GO-based gas separation membranes, however, remains challenging, although a few preparation approaches have been reported. Here in this work, we present for the first time that the co-solvent ink-jet printing, as a fast and scalable method, can be utilized for scalable GO-based gas separation membrane preparation. Large-area (>100 cm 2 ), ultrathin, and high-quality GO membrane was successfully deposited on commercial polysulfone (PS) support, and characterized by scanning electron microscopy, X-ray photoelectron spectroscopy, Fourier transform infrared spectroscopy, and X-ray diffraction, et al., Selective hydrogen (H 2 ) and helium (He) transport over carbon dioxide (CO 2 ) and nitrogen (N 2 ) was demonstrated for the printed GO membrane. To further explore the separation potential of the printed GO-based gas membrane, additives for facilitated molecular transport were incorporated during the membrane printing process. By inserting CO 2 -philic agents into the printed GO membrane, highly efficient separation of CO 2 from N 2 was achieved with CO 2 /N 2 selectivity of 70 and CO 2 permeance as high as 2,500 GPU. The strategy proposed here may provide guidance for large-scale GO-based gas separation membrane production and a versatile approach for applying other functional 2-dimensional materials towards the membrane separation application.

42 ENGINEERING↗
DOE OSTI2025

Physical model and experimental validation of a high temperature proton exchange membrane electrochemical hydrogen pump cell for efficient single-stage extraction of low concentration hydrogen gas

There is interest in valorization of existing natural gas infrastructure to facilitate the co-transportation of hydrogen via blending of hydrogen gas initially at limited concentrations of 1–20 vol% H2 and to subsequently extract hydrogen at fuel cell quality standards (SAE J2719/ISO14687-2). High temperature proton exchange membrane electrochemical hydrogen pump (HT-PEM EHP) based on phosphoric acid doped polybenzimidazole (PA-PBI) exhibits good performance at elevated temperatures (>120 °C), which provides desirable tolerance to non-methane natural gas constituents that are problematic for lower temperature based EHP. To better understand the suitability of the HT-PEM EHP for such gas separation processes, a two-dimensional model of EHP based on PA-PBI was developed. The model is validated for several relevant operating conditions and across cells with differing amounts of phosphoric acid content in the electrodes. Operando micro x-ray computed tomography (CT) imaging of an HT-PEM EHP was used to further validate physical parameters and assumptions of the model. The impacts of pressure, relative humidity of the anode feed, and concentration of feed gases on separation performance are investigated. This study shows that a specific energy of separation of 5.1 kWh/kg H2 at a hydrogen recovery factor (HRF) of 50 vol% can be achieved in a single stage with the EHP, producing fuel cell quality hydrogen purity of 99.99 vol% H2 from a 2 vol% H2/CH4 feed blend, while pressurizing the product H2 at a pressure ratio of 1.3 relative to feed pressure.

Stansberry, John M↗
DOE OSTI2022

Chemical and isotopic evolution of flowback fluids from the Utica Gas Shale Play, Eastern Ohio USA

For this work, hydraulic fracturing flowback fluids were collected from two Utica/Point Pleasant well pads in eastern Ohio. One site was in the wet gas zone (UPPW), while the site ~50 km south consisted of four wells on the same pad in the dry gas zone (UPPS). Samples of input fluids also were collected before and during hydraulic fracturing. Flowback fluids are Na-Ca-Cl brines with total dissolved salt (TDS) concentrations that increase over several months from ~100 to 200 g/L. The slightly higher TDS of the dry gas fluids are in part due to recycled flowback used as input fluids, and in part due to lower volume of water used in hydraulic fracturing. Concentrations of most major ions (Ca 2+ , Mg 2+ , Na + , Sr2 + , Fe, Mn, Cl – , Br – ) are similar for the five wells sampled, although small but systematic changes occur in the major element ratios over time. Most notably, an increase in the Sr/Cl ratio corresponds to an increase in the 87 Sr/ 86 Sr ratio in the fluids, suggesting interactions with a more radiogenic Sr source in the subsurface. Dissolved Ba concentrations and Ra activities were different between the two sites, reflecting a high SO 4 2– fluid used at the UPPW site, and water-rock reactions occurring during hydraulic fracturing at the UPPS site. Water oxygen (δ 18 O) and hydrogen (δD) isotopes for input fluids used in the UPPW4 well and fresh water used for the UPPS wells fall on the Global Meteoric waterline (GMWL). Flowback fluids from both sites are relatively enriched in δ 18 O and δD compared to the input, but do not appear to follow a simple mixing trend, suggesting reaction and isotopic exchange with carbonates and fractionation due to imbibition in the rock. Cl isotopes, δ 37 Cl in the FP fluids varied from ~ –0.43 to +0.13‰, the largest variation was observed in the earlier stages of flowback, while in the later stages δ 37 Cl exhibited a small but systematic increase over time, suggesting diffusion control of isotopic composition. Some of the trace species measured (dissolved Fe, Mn, thiosulfate and organic acids) do not follow the same trends as the major ions, suggesting contributions from input fluids, or microbially mediated reactions are exerting control on their concentrations. Input water chemistry exerts an important control on the Sr and Ba concentrations in flowback water. High SO 4 2– in the input fluids used for hydraulically fracturing the wet gas well leads to precipitation of barite-celestite in flowback fluids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

The effect of stress on the migration of He gas bubbles under a thermal gradient in Fe by phase-field modeling

Here a phase-field model is parameterized to study the effect of elastic stresses on the migration of He gas bubbles in Fe under a temperature gradient. Stresses caused by the gas bubble pressure and residual stress in the Fe matrix are considered. The dependence of He bubble migration velocity on the magnitude of the residual stress, average temperature, temperature gradient, and bubble size is measured. In agreement with a theoretical model based on surface diffusion, simulation results demonstrate that He bubbles move towards the high temperature region with velocities in Fe that are orders of magnitude faster than previously reported in UO 2 . It is found that local stresses in the matrix caused by the He bubble have negligible effect on the bubble migration process; however, residual stresses in the Fe matrix, potentially caused by processing or irradiation, can modestly modify bubble kinetics through pressure dependence of the He diffusion coefficients. Compressive residual stress decreases diffusion coefficients for bulk and surface diffusion mechanisms, thus reducing the migration velocity of the gas bubble. In contrast, tensile residual stress increases the diffusion coefficients, resulting in an increase in the gas bubble migration velocity. This pressure dependence is also consistent with a theoretical model. This phase field model lays the foundation for analysis of bubble coalescence-induced fracture in He bubble-containing steels.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Adaptations for gas exchange enabled the elongation of lepidopteran proboscises

The extensive biodiversification of butterflies and moths (Lepidoptera) is partly attributed to their unique mouthparts (proboscis [Pr]) that can span in length from less than 1 mm to over 280mm in Darwin's sphinx moths. Lepi-doptera, similar to other insects, are believed to inhale and exhale respiratory gases only through valve-like spi-racles on their thorax and abdomen, making gas exchange through the narrow tracheae (Tr) challenging for the elongated Pr. How Lepidoptera overcome distance effects for gas transport to the Pr is an open question that is important to understanding how the Pr elongated over evolutionary time. Here, we show with scanning electron microscopy and X-ray imaging that distance effects on gas exchange are overcome by previously unreported micropores on the Pr surface and by superhydrophobic Tr that prevent water loss and entry. We find that the density of micropores decreases monotonically along the Pr length with the maxima proportional to the Pr length and that micropore diameters produce a Knudsen number at the boundary between the slip and transition flow regimes. By numerical estimation, we further show that the respiratory gas exchange for the Pr predominantly occurs via diffusion through the micropores. In conclusion, these adaptations are key innovations vital to Pr elongation, which likely facilitated lepidopteran biodiversification and the radiation of angiosperms by coevolutionary processes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Optimizing conformance control for gas injection EOR in unconventional reservoirs

Field observations have shown that interference between wells caused by connected fractures commonly exists in unconventional reservoirs. The well interference effect and conformance issues could lead to minimal enhanced oil recovery response (EOR) in actual operations if they are not properly controlled. A series of data analysis, modeling, and experimental activities were performed in this study to investigate the gas EOR strategies in the Bakken Formation. Employing the embedded discrete fracture modeling technology, a multiple-well, multiple-fracture model was developed to capture the well interference and conformance issues in the Bakken. The model made it possible to investigate the complex flow behavior between wells in the EOR (huff ‘n’ puff) processes. Alternative EOR and conformance control strategies using water and surfactant injections were studied to improve oil production performance based on experimental observations. Results showed that water injection could be used for conformance control in the Bakken because of its relatively low mobility compared to gas; however, water could also block oil flow around the conformance control wells because of the high interfacial tension between oil and water. Adding surfactant to the injection water is more effective for improving gas EOR performance since surfactant reduces the oil–water interfacial tension and contact angle effectively. Up to 9.4% more oil could be produced from the huff ‘n’ puff wells in 2 years of EOR operations when rich gas was injected at only 3 MMscf/d with 6000 psi of surfactant injection in the offset wells for conformance control.

42 ENGINEERING↗
DOE OSTI2020

Growth of Jupiter: Formation in disks of gas and solids and evolution to the present epoch

The formation of Jupiter is modeled via core-nucleated accretion, and the planet's evolution is simulated up to the present epoch. Throughout the phases when the planet acquires most of its heavy-element content, the calculation of solids' accretion accounts for interactions with an evolving disk of planetesimals. The phase of growth from an embryo of a few hundred kilometers in radius until the time when the accretion of gas overtakes solids' accretion was presented by D'Angelo et al., and the same numerical methods are applied here. Those calculations followed the formation for about 4 × 10 5 years, until the epoch when the heavy-element and hydrogen/helium masses were $M_Z ≈ 7.3$ and $M_{XY} ≈ 0.15$ Earth's masses ($M_⊕$), respectively, and $\dot {M} _{XY} ≈ $$\dot {M}_Z$. In this work, the calculation is continued through the phase when $M_{XY}$ grows to equal $M_Z$ , at which age, about 2.4 × 10 6 years, the total mass of the planet is $M_p ≈ 20 M_⊕$. About 9 × 10 5 years later, $M_p$ is approximately $60 M_⊕$ and $M_Z ≈ 16 M_⊕$, three-quarters of which are delivered by planetesimals larger than 10 km in radius. Around this epoch, the contraction of the envelope dictates gas accretion rates a few times 10 –3 $M_⊕$ per year, initiating the regime of disk-limited accretion, whereby the planet can accrete all the gas provided by the disk, and its evolution is therefore tied to disk's evolution. Growth is continued by constructing simplified models of protosolar accretion disks that evolve through viscous diffusion, winds, and accretion on the planet. Jupiter's formation ends after ≈ 3.4–4.2 Myr, depending on the applied disk viscosity parameter, when nebula gas disperses. The young Jupiter is 4.5–5.5 times as voluminous as it is presently and thousands of times as luminous, ~10 –5 $L_⊙$. The heavy-element mass is ≈ 20 $M_⊕$. The evolution proceeds through the cooling and contraction phase, in isolation except for solar irradiation. After 4570 Myr, the age of the solar system, radius and luminosity of the planet are within 10$\%$ of current values, accounting also for uncertainties in the power absorbed from the Sun. During formation, and soon thereafter, the planet exhibits features, e.g., luminosity and effective temperature, that may probe aspects of the latter stages of formation, if observable. These possibly distinctive features, however, seem to disappear within a few tens of Myr.

79 ASTRONOMY AND ASTROPHYSICS↗